Flush Draw vs. Overpair: The Numbers Street by Street

An overpair against a flush draw on the flop is roughly a 62% to 38% matchup. With K♠ K♦ against Q♥ J♥ on a 9♥ 4♥ 2♣ board, the kings win 616 of the 990 possible turn and river combinations, and the flush draw wins the other 374. Neither hand is a lock, and the numbers change sharply with each card that falls.

This article follows that one hypothetical hand street by street. It shows where the 37.8% for the draw comes from, how the equity moves after a blank, a pairing card, a heart and a king on the turn, and how the price of a call compares with the draw’s chance of winning. All figures come from counting every possible runout, and the hand is invented for illustration. Readers who want the basic idea of counting cards that help can start with what outs are in poker.

The Matchup and What Each Hand Needs

An overpair is a pocket pair higher than every card on the board. K♠ K♦ is an overpair on 9♥ 4♥ 2♣ because the highest board card is a nine. Right now the kings are ahead, holding the best pair on the table.

The opponent holds Q♥ J♥, two hearts, and the board already shows 9♥ and 4♥. That makes four hearts in view and a flush draw, since any one more heart gives a five-card flush. The queen and jack add little by themselves: pairing either card still leaves the opponent below the kings, though both together would make two pair.

To count correctly, every card that is visible must be removed from the deck. Four hole cards and three board cards are known, so 52 − 4 − 3 = 45 cards are unseen. This is the viewpoint of someone who can see both hands, which is how an equity calculation works. A player who sees only one hand would count 47 unseen cards instead, because the opponent’s cards are still unknown to that player.

Flop Equity: Where 62.2% and 37.8% Come From

Equity is the share of all possible runouts that a hand wins. With two cards still to come from 45, there are C(45,2) = 990 runouts. The kings win 616 of them and the flush draw wins 374, with no ties, so the kings hold 616 ÷ 990 = 62.2% and the draw holds 374 ÷ 990 = 37.8%.

Step one: the flush alone

Hearts total 13, and four are visible (9♥, 4♥, Q♥, J♥), so 9 hearts remain among 45 cards. The chance of at least one heart in two cards is 1 − (36 ÷ 45) × (35 ÷ 44) = 1 − 1,260 ÷ 1,980 = 36.4%. That equals 360 of the 990 runouts. The rule of 4 estimates 9 × 4 = 36%, a close approximation here because the number of outs is moderate.

Step two: the corrections

The 37.8% is not simply 36.4%, because two effects pull in opposite directions. Some flushes lose, and some non-flush runouts win. The table splits all 990 runouts by result.

The 27 non-heart wins are specific. A ten with an eight, or a ten with the K♣, completes a straight for the opponent (9 + 3 = 12 runouts). A queen with a jack gives two pair (9 runouts), and two queens or two jacks give three of a kind (3 + 3 = 6 runouts). Net of the 13 flushes that lose, the extra 27 add 14 runouts, which is 1.4 points and explains why 36.4% becomes 37.8%.

Worked Example: Four Possible Turn Cards

Once the turn is dealt, one card remains and 44 cards are unseen. Equity after the turn is a simple count of the river cards that win for each hand. The table shows four different turn cards on the same flop.

On the 7♦ the flush draw needs one of 9 hearts, so its chance is 9 ÷ 44 = 20.5%, about 3.9 to 1 against. The 9♦ pairs the board and changes one detail: the K♥ would still complete a heart flush, but it also gives the kings three kings and a pair of nines, a full house that beats the flush, so only 8 of the 9 hearts win for the draw.

The K♥ turn gives the kings three of a kind, but the flush is already made, so the kings need to improve. They win with the K♣ (four of a kind) or with any card that pairs the board, which gives a full house: three 9s, three 4s and three 2s. That is 1 + 9 = 10 winning cards, and 10 ÷ 44 = 22.7%. A made flush leaves the kings almost dead, and on the 5♥ turn they have no winning river at all.

A consistency check confirms the table. Adding the kings’ wins over all 45 possible turn cards gives 1,232, which is 2 × 616, because each two-card runout can arrive in two orders. The street-by-street figures therefore agree with the flop equity.

Reading the Number at the Table: Equity Against Price

The same equity can be set beside the price of a call. Suppose the pot is 100 on the flop and the overpair bets. The draw’s required equity is the call divided by the pot after the bet plus the call, a formula covered in the guide to how to calculate pot odds. The break-even equity is bet ÷ (100 + 2 × bet).

This comparison uses equity alone and ignores chips that may be won or lost later. On the turn the picture tightens. After a flop bet of 50 and a call, the pot is 200. On a 7♦ turn, a bet of 100 gives a price of 100 ÷ (300 + 100) = 25.0%, while the draw has only 20.5%. The shortfall of 4.5 points means the call needs about 100 ÷ 0.2045 − 400 = 89 chips of extra winnings to break even, a figure explained in the article on implied odds in poker.

The percentages are exact for this hand and these cards, yet the bet sizes and the pot are assumptions. A different pot or a different opponent holding would change every row.

Common Mistakes With This Matchup

Using 47 unseen cards is the first mistake when both hands are known. With both hands visible, 45 cards remain, and using 47 shifts every percentage slightly.

Assuming every heart wins overstates the draw. When the board pairs, a heart can give the overpair a full house, as the K♥ does on the 9♦ turn. Counting such cards as clean outs ignores the fact that some outs are dirty.

Forgetting the non-flush wins understates the draw. A ten and an eight, or a queen and a jack, still beat the kings without any heart. They add 2.7 points to the draw’s equity.

Treating the flop equity as a turn equity misleads in both directions. The flop figure is an average over 45 turn cards, and the actual turn equity ranges from 0.0% to 100.0% in the table above.

Reading 62.2% as a prediction is the last. The kings win about 6 times in 10 on this flop and lose the other 4, so any single hand can go either way.

Why These Numbers Matter Beyond One Hand

The same pattern holds for many overpair-versus-draw confrontations. An overpair is a moderate favorite against a flush draw, and the exact split depends on the other cards the draw holds and on the board, which is why a calculator that enumerates runouts, rather than a rule of thumb, is the dependable tool, as described in how poker equity calculators work.

Equity also shifts most on the turn. From 62.2% on the flop, the kings can move to 79.5% on a blank or fall to 0.0% on a heart. That swing is the main reason a draw is called a drawing hand: its value comes from a small number of cards. Probabilities describe the long run, and poker involves real financial risk, so none of these figures guarantees a result in a single session.

Related Concepts and the Next Step

This matchup pairs naturally with two others. The comparison of a set against a flush draw, in set vs. flush draw, street by street, shows how a stronger made hand changes the split, and the overpair vs. open-ended straight draw analysis shows how a different draw behaves against a pair. Reading all three side by side builds a feel for the numbers.